Talk:Gauss–Bonnet theorem

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Mathematics rating:	Start Class	High Priority	Field: Geometry
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Needs illustrations, history, applications, examples. Tompw 19:25, 7 October 2006 (UTC) Needs citations to get to B class. Salix alba (talk) 10:14, 3 November 2006 (UTC)

[edit] What about the generalized version?

I have started Pfaffian, so maybe someone can do Generalized Gauss-Bonnet theorem??? Tosha 05:52, 16 Mar 2004 (UTC)

[edit] A and s

What is A and what is s in the formula?

A is a differential-2-form, which represents the "surface" of the manifold M. Simililarly, s is a one-form (also called Pfaffian form), which represents the border of M (which is one-dimensional).

[edit] Orientable?

Does the manifold really have to be orientable? AxelBoldt 01:07, 21 April 2006 (UTC)

I don't think so. AFAIK, it just must be able to be triangulated (to get the Euler characteristic), but other than that there are no requirements on the surface. cBuckley (Talk • Contribs) 17:37, 21 April 2006 (UTC)

The Russians also don't mention orientability [1], so I'll make the change. AxelBoldt 01:06, 23 April 2006 (UTC)

[edit] Move application section?

It seems to me the application section should be moved since it's really just an application of Euler's formula. The Gauss–Bonnet theorem is only used to show that the Euler characteristic of the sphere is 2 and there are much more elementary ways of doing that. --RDBury (talk) 01:37, 29 February 2008 (UTC)